The coil in Fig. 28-50 carries current i=2.00 A in the direction indicated, is parallel to an x

step 1 In this question, we have this setup. So we have three tons of circular coil carrying current 2m

The coil in Fig. 28-50 carries current i=2.00 A in the...

The coil in Fig. $28-50$ carries current $i=2.00 \mathrm{~A}$ in the direction indicated, is parallel to an $x z$ plane, has $3.00$ turns and an area of $4.00 \times 10^{-3} \mathrm{~m}^{2}$, and lies in a uniform magnetic field $\vec{B}=(2.00 \hat{\mathrm{i}}-3.00 \hat{\mathrm{j}}-4.00 \hat{\mathrm{k}}) \mathrm{mT} .$ What are (a) the orientation energy of the coil in the magnetic field and (b) the torque (in unit-vector notation) on the coil due to the magnetic field?

The coil in Fig. $28-50$ carries current $i=2.00 \mathrm{~A}$ in the direction indicated, is parallel to an $x z$ plane, has $3.00$ turns and an area of $4.00 \times 10^{-3} \mathrm{~m}^{2}$, and lies in a uniform magnetic field $\vec{B}=(2.00 \hat{\mathrm{i}}-3.00 \hat{\mathrm{j}}-4.00 \hat{\mathrm{k}}) \mathrm{mT} .$ What
are (a) the orientation energy of the coil in the magnetic field and
(b) the torque (in unit-vector notation) on the coil due to the magnetic field?

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Key Concepts

Torque on a Magnetic Dipole

The torque on a magnetic dipole in a uniform magnetic field is the measure of the force acting to align the dipole with the field. This torque is given by the cross product of the magnetic dipole moment and the magnetic field, expressed as ? = ? × B. The resulting torque causes the dipole to rotate, aligning it with the magnetic field direction.

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity that characterizes the strength and orientation of a current loop in a magnetic field. For a coil, it is defined as the product of the number of turns, the current flowing through the coil, and the area of the coil, with the direction given by the right-hand rule. It provides a measure of how the coil interacts with external magnetic fields.

Magnetic Potential Energy

The magnetic potential energy of a dipole in a magnetic field quantifies the energy associated with the orientation of the magnetic dipole moment relative to the magnetic field. It is calculated using the dot product of the magnetic moment and the magnetic field, typically expressed as U = -? · B, indicating that the energy is lowest when the dipole aligns with the field.

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